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# An electric field of intensity 3.50 kN/C is applied along the x - axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if (a) the plane is paral- lel to the yz - plane, (b) the plane is parallel to the xy - plane, and (c) the plane contains the y - axis and its normal makes anangle of 40.0° with the x - axis.

## a. $857.5 \mathrm{N} . \mathrm{m}^{2} / \mathrm{C}$b. 0c $657 \mathrm{N} . \mathrm{m}^{2} / \mathrm{C}$

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### Video Transcript

in this problem. On the topic of electric forces and fields, we are told the electric field strength that is applied along the X axis through a rectangular plain with given dimensions. We want to calculate the electric flux through this plane if the plane is parallel to the Y Z plane. The plane is parallel to the XY plane and finally the plane contains the Y axis and it's normal. Makes an angle of 40 degrees with the X axis. So firstly, we know the anger. The area of this rectangular plain A is equal to zero 0.35 m times the other dimension zero point 7 m, which gives us, you know 0.245 meters squared. So in part A. If the plane is parallel to the wise, it plain it's normal line is parallel to the X axis and makes an angle. Detail is equal to zero with the direction of the field, so the electric flux, then five e is equal to E. A. Times costs Peter, which is the electric field strength. The 0.5 times 10 to the three Newton's cool um, time zero point 245 m squared, which is the area EMC cosign of zero degrees. So this is simply 800 and 58 Newton meters squared. Coolum. That's the electric flux when the plane is allowed to the wise it plain next for Part B, when the plane is parallel to the X axis we have, theater is equal to 90 degrees and therefore cost. Theater is the cost of 90 degrees, which is zero. And that means that the electric flux fiery using the equation above will also be zero. And lastly for part C, we know from above that the electric flux Phi is equal to electric field strength. E times a Times callsign theater. The electric field strength is constant. The 0.5 times 10 to the power three Newtons per column multiplied by the selfish area. 0.245 meters squared times the angle in this case because of the angle cost of 40 degrees. So calculating we get the electric flux to be 657 Newton meters squared, cooler

University of Kwazulu-Natal